Problem Frames are a systematic approach to the decomposition of problems that allows us to relate requirements, domain properties, and machine specifications. Having decomposed a problem, one approach to solving it is through a process of composing solutions to sub-problems. In this paper, we contribute to supporting such a process by providing a way to compose multiple Problem Frames. We develop a systematic approach to composing inconsistent requirements. We introduce Composition Frames, a requirements construct that models relevant aspects of composition and thus deals with unwanted effects, such as interference of overlapping reactions to events. Throughout the paper we use a simple case study to illustrate and validate our ideas.